SCIENTIFIC ABSTRACT BELYAYEV, V. F. - BELYAYEV, V. I.

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CIA-RDP86-00513R000204610019-8
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100
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December 31, 1967
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"APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 Autoxidation of 1-isopropyl-cyclohexene-1 .... s/5 Po/6 ~/ooo/ooa/oog/o ~6 AO57/Ai26 radical. Hence, the most reactive group in autoxidation is tho methylene group near the alkyl radical. Tile latter increases the mobility of the hydrogen atom in the adjoining methylene group. Autoxidation experiments of 1-iso~ropyl_ -cyclohexene-1, at 68�C, during 6 h, carried ou't in the presence of ~he initiators cobalt stearate, acetate, .%~,aiate, manganese stearate and formiate, or kaolin shov;ed that the cobalt compounds have the greatest activity, but also docomposa the hydroperoxide which gm?rates during autoxidation. In the presence of manganam~ ,.nd cobalt formiate the rate of autoxidation is smaller th~mn without addizio:-, of initiator. A new hydroperoxide was synthesized by liquid-phase low-temperature au%oxidation of 1-isopropylcyclohexene_l and determined as 1-isopropylcyclohezene_ -1-hydroperoxide_6. Autoxldation of 1-ethy!-cyclopentene_l was carried out at 60�C during 5 days without initiator and ~he following ne~ hydroperoxide separated: !-ethylcyc!opentene-l-hydroperoxide_5. This compound is stable during long-last- ing storage. ~nere are ~ tables. Card APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 ~-LYA~EV, V.F. Autoxidation of 1.isopropyl-l-cyclohexene and 1-ethyl-1- cyclopentene to hydroperoxides. ~hidkofaz.okisoneproorgo soed. no.1:97-104 '61. (~L~J, 15:2) (Cyclohexene) (Cyclopentene) (Hydroper~ides) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 KOCHETKOV~ NoKo; BELY~iYEV~�.F.; DUD]2~;~.~ G.S. Ketovinilation of nitrocyclohe~neo Zhuroobokhimo 32 nOo6:1785-1789 Je '62. (~RA 1~:6) 1. Belorusskiy gosudarstvennyy universitet. (Cyclohexane) (Vinylation) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 BELYAYEV, V.F.; YATSEVI~lt, N.M.; SOEDLOV, N.A. Synthesis of chalcones on the base of ~ - chlorovinyl ketcheS. Part 2. Zhur.oh. kbim. 32 no.6:2022-2025 Je '62~ (MIRA 15:6) 1, Belorusskiy gosudarstvennyy universitet ira. V.I.Lenina. (Chalcone) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 BEL~A~EV~ ~.F, Ketovinylation of nitroparafflns. Zhur. VKItO 9 no. 3~358 '64. (MIRA 17,9) 1. Belorusskiy gosudarstvennyy universitet imeni Lenina. APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 BELYA~V, V.F. Synthesis of chalcones on the basis of~-chlorovinyl ketoneso Zhur. ob. kh~. 34 no. 3:861-864 ~!r t6&. (ML~J~ 17:6) 1. Belorusskiy gosudarstvennyy uniYersitet im~ni V.I.I~nina, APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 BELYAYEV, V. G. ~ . ~Analysis of a Systam of Caving-In in Layers and ~tho~s of Perfecting It in the Process of Working Polymetallic and Copper-Pyrite Deposits.~ Min Higher Education USSR. Moscow Inst of Nonferrous Metals and Gold imeni M. I. Kalinin, Moscow, 1955. (Dissertation for the Degree of Candidate in Technical Sciences.) So; ' z Let s' No 3, 1956 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 1.Severokavkmzskiy ogrnometallurgicheakiy institut, Eaffedra razrabetki poleznyt~h iskopa~emkuh. (Boring machiner~) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C~A-RDP86-005~3R0002046~00~9-8 1. Severolcavkazmki~ goraometallurgtoheekiy inet[tut. Xafedra rasrmbotkt memtoroshdenty polesn.vkh tmkopayem~kb. (~adon region--Mining ~negtneering--Oosts) (Ore dressing--Costs) APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 BELYAYE~, V.G.; VEDERNIKOV, I.I.; GONCHAROV, V.N.; PATE!~L"~, A.Kh.; Rb/.'JANTSEVA, M.B., red.; FORMALI]~IA, Ye.A., tekhn, red. [Using high-frequency current for defrosting frozen sprat briquets] Defrostatsiia briketov morozhenoi kiltki tokom promvshlennoi chastoty. Moskva, Izd-vo zhurnala "Rybnoe khoztaistvo" VNIRO, 1962. 21 p. (MIRA 17:3) 1. Sotrudniki Kaspiyskogo nauchno-issledovatel'skogo in- stituta morskogo rybnogo kho~,aystva i okeanografit, Astrakhan' (for Belyayev, Vederniko�). APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 BELYAYE~, V.G.~ BORISENKO, G.A. Profiling the ball-~eturn channel for ball transmissions. Stan. i instr. 35 no.6:13-16 Je '6~ (MIRA 17~8) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C~A-RDP86-005~3R0002046~00~9-8 APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 .... BELYAYEV~ V.G. Case of neurodermatftis complicated by a mass attack cf ohicken mites. Med. pa~az, i paraz, bol. 3~ no.1:116-t17 Ja-F ~65. ]. Prtmorskaya krayevaya prottvochmmnaya stants~ya, Ussurtysk. APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 KORNIYENKO, A.M.; SHTEL'MAKHOV, M.S.; GEYLER, Z.Sh.; BERESNEV, V.~.; KOTLIK, S.B.; GORFINSKIY, EI~.M.; ZEL'DIN, Yu.R.; KURGIN, Yu.M.; BELYAYEV, V.G.; Z~K, P.S.; ZAYTSEV, A.A.; LI, A.M.$ SKVORTSOV, LuTTS~-'R.R.; KHVINGIYA, M.V.; NINOSHVILI, B.I.; SE~tENCH~';KO, D.I.; SUKHANOV, V.B. Soviet inventions in mechanical engineering. Vest.mashinost~'. 45 no.11:~7-~8 N '65. (MIR~ 18:125 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C%A-RDP86-00513R000204610019-8 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 EELYAYEV, V.I., kand. tekhn.nauk. Sinking screw piles. Art.der. 20 ne.7:24-25 J1 (Piling (Civil engineering)) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 ~ELYAYEV, Valentin Ivanovich$ MIR0SHNIC}IENKO, V.D., red. izd-va; SP~LYAR, s~Ya'.'~-'teklm'."red~[~L~i~lLI~A~ L.N., tekhn, red. [Practices in planning and analyzing coal production costs] Prak- tika planirovaniia i ,~-11za sebestoimosti dobychi uglia. Moskva, Gos.nauehno-te~bn. izd-vo lit-fy po gornomu delu, 1961. 207 p.. (~ 14:6) (Goal ~d.nes a~nd m{,~{~;--Oosts) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 B~JuTAYEV. V'. !. � k~and. ~ekhn. nauk F~fect of underloading and successive overloadings, on the fatigue strength of steels, ~ash. Bel. no.6~94-110 ~59. (~IRa 13~6) (Steel--Testings) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 PHASE I B00KEXPLOITATION SOV/610? � Belyayev, Vasiliy Ivanovich Issledovaniye protsessa ustalosti metallov (Investigation o� the Metal Fatigue Process). ~insk, Izd-vo NVSE i PO B~ER, 1962. 109 p. Errata slip inserted. 2700 copies printed. Ed.: V. T. Nekhay; ?ech. Ed.: A. P. Dubovik. P~w0~M:' The book may be useful to scientists, machine designers, and stud~n~. 0OVERAGE: The book deals with metal fatigue and discusses the effect of various'test conditions on the enduranoe limit and service life of carbon and alloy steels and nonferrous metals. The effect of limit load t~pe, the strain rate, and the size factor (scale effect)is also analyzed. .Th9 assistance of Professor T. A. Lebedev is acknowledged. There a~e 55 references:. 52 Soviet, 2 English, and ~ French. cma APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8 _ "T.,e use of bbproduct steel powder from ball be&ring proauction in ?owder metallurgs-." report submitted for Intl Conf on Powder MetallurG;,, New �ork� i~-!7 Belorussian Pol,,%ecnical Inst~ Minsk. APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8 APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 AUTHORS: Kolesnikov,A.G.,and Belyayev,V.I. SOV/155-58-2-42/47 TITLE: On the Crystallization of a ~r oooled Cloud on Interspersed Artificial Sublimation Center~ (0 kristallizatsii pereokhlazhdennogo oblaka na iskusstvennykh yadrakh sublimatsii, vvedennykh v nego putem zaseva) PERIODICAL: Nauchnyye doklady vysshey shkoly. ~iziko-matematicheskiye nauki, 1958, Nr 2, pp 200-205 (U$$R) ABSTRACT: The authors consider the ieothermio crystallization of a cloud consisting of water vapor and water drops cooled to ca. -lO�G, the micrdstructure of which is independent of the local coordinates, and in which to a given moment a large set of sublimation kernels is interspersed. The authors establish a system consisting of six equations out of which tha number-of appearing crystals, the vapor concentration, and other charaoteristics of the sublimation process can be obtained as fuactions of the time. There is 1 figure, and ~ referenoes, 2 of which are Soviet, and 1 American. ASSOCIATION~Moskovskiy gosudaratvennyy universitet imeni M.V. Lomonosova (Moscow State University lmeni M.V.Lomonosov) APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 AUtHOr3 ~ TITLE~ PE1LIODICAL~ ABSTP~CTs ~ ~ cr~-llization of a cloud under an influence of CO2 on the Card 1/2 Kolesnikov, AoG. Belyayev, VoI. SOV/155-58-4-32/34 On the Calculatio~-~ ~'h�-~%e of Crystalline Growth ~f an Undercooled Cloud Under Influence of Hard Carbonic Acid (K raschetu skorosti kristalli~atsii pereokhlazhdennogo . obI~a'pri vozdeystvii na nego tverdoy uglekisl~t-~y) Nmla~'doklad~ vysshey shkolyo Fiziko-matematicheskiye nauki, 1958, Nr 4, PP 199 - 206 (USSR) The authors propose to calculate the process of artificial basis of %he following simple scheme : The process is under- stood as a diffusion of ice particles arising under the in~. fluence of hard carbon digxide, and as the dlaiillation of water from the drops on the ice crystals� The calculation according %o this scheme is carried out under the simplest assumptions (horizontal~ thin~ infinite cloud ; linear diffusion of CO2 otc). It is proposed to verify experiment- ally the obtained formulas in order to obtain indications for those facts which are not taken into account in the/ APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 On'~he Calculation of the Rate of Crystalline Growth SOV/155-58-4-52/34 of an Unde=ccoled Cloud Under Influence of Hard Carbonic Acid Gas scheme. A numerical example is given. There are 2 figures, and. 3 Soviet references� ASSOCIATIONs Moskovskiy Sosudarstvennyy universitet imeni M.Vo Lomonosova (~oscow State University imeni Z~oVo Lomonosov) ~ SUBMITTED:' April 5, 1958 Card 2/2 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 AUTHORSs TITLE~ PERIODICAL~ ABSTRACT: Card 1/ $ Kolesnikov, A.G., ~~Ij~..,~ SOV/155-58-5-19/~7 On the Calculation of the Rate of Crystalline Growth of a Supercooled Cloud Under Influence of Ice-Forming Particles Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye nauki,1958,Nr 5,PP 102-107 (USSR) The paper consists of an introduction (section 1) in which the author refers especially to the papers of V.Ya.Nikandrov~ G.M. Bashkirova, P.N. Krasikov and others, and of 2 further sections. In section 2 he considers the onedimensional problem analogously to L'Ref 11_7 : In the starting moment the ice-forming particles are in a vertical plane and then diffuse in horizontal direction, whereby simultaneously crystals are formed on them. For the steam influx to the crystals the author obtains q2 = 4*D(u-u2) ld'~2 I n2~2dx2 o -(2) by similar considerations as in L-Ref 11_7, where j APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 19 On the Calculation of the Rate of Crystalline Growth SOV/155-58-5-19/~7 of a Supercooled Cloud Under Influence of Ice-Forming Particles Card 2/3 (x-x2)2 r max � 2(x2,~2) = I W~u(x2,~2), r3tg(r~,x2,~2)dr~ o Here u denotes the steam concentration, r2 medium size of the crystale in the point x in the moment ~, E the coefficient of turbulent diffusion, D the coefficient of molecular steam diffusion, x2 the initial coordinate of the crystal originated in the moment ~2 ' W the probability of the formation of ice crystals on the particles, ~ the density distribution function, APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 On ~he Calculation of the Rate of Crystalline Growth SOV/155-58-5-19/37 of a SuPercooled Cloud Under Influence of Ice-Forming Particles r3 magnitude of the parti~le. In section 3 the author tries to extend the obtained results to the two-dimensional case occurring in natural situations. There are 13 references, 8 of which are Soviet, 2 English, 2 Japanese, and ~ American. A:~SOCIATION: Moskovskiy gosudarstvennyy universitet imeni ~.:.V.Lomonosova (Moscow State University imeni M.V. Lomonosov) ~;~B~'~TTED: .May 8, 1958 ~/ APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 :9-58-5-7/15 AuTHoRS: Kolesnikov, A. G. and Be~, V. I. TITLE~ The Crystallization of Super-cooled Water Clouds by Freezing of Drops (O l~istallizatsii pereokhlazhdenno�o vodnogo oblaka putem zamerzantya kapel') PERIODICAL: IzvestiyaAkademii Nauk SSSR~ Seriya Geofizicheskaya~ 1958~ Nr 5, PP 636-642 (USSR) .ABSTRACT: Ref.1 considers the process of crystallization of super- cooled water vapour when crystals arise on sublimation nuclei~ This would occur in seeding experiments, but in natural pro- cesses it is more likely to occur by freezing of the water droplets. It is assumed that the cloud is homogeneous (i~eo, the functions used do not depend on coordinate) so that cal- culations can be made per unit volume. At the start the cloud consists of water vapour and drops in dynamic equilibrium. It is assumed that at a certain time, due to a change in tempera- ture,, etco~ metaBtability occurs. This moment is taken as the onse~ of crystallization. Since the saturation vapour pressure is lower over ice than water, the ice crystals grow at the expense of the water vapour. This loss of water vapour causes the unfrozen drops to evaporate and the process continues till the whole cloud has frozen. The freezing process occurs almost Card 1/~'nstantly that a seed crystal appesrs. The probability of APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 zI~9-58-5-7/15 The Crystallization of-,~uper-cooled Water Clouds by Freezing of ~ropso appearance seed crystal in unit volume of fluid is a function of temperature (Ref.2). Taking the process to be isotherma~ " the probability of freezing is proportional to the vol~ue~ Thus~ if n~ drops freeze/unit time from n drops (the s~ne size) then: n' = ~vn (1) where ~ = const, v is the volume of a drop. Since the initial dimensions of cloud droplets are small and crystals at this stage do not grow to a large sizeG the evaporation of drops and the growth of crystals can be considered to be con- trolled by molecular diffusion of water vapour. To describe this change ~axwell's equation is used for drops (Eq.2) and crystals (Eq.~)o (Where rI is the radius of-a drop; uI is the vapour concentration corresponding to equilibrium of vapour and drops; r2 and u2 are the same quantities for a crystal; D is the molecular diffusion coefficient for the vapour; ~l and ~2 are the densities of water and ice; u is the vapour concentration in the absence of drops and crystals) uI and Card 2/9 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 ~9-58-5-7/15 ~e Crystallization of Super-cooled Water Clouds by Freezing of Drops� u2 are considered constant. Since at the initial moment, the drops are in equilibrium with the vapour, therefore u(O) m Ul . If the radius of the drops at this moment is R1, then its radius at any later moment will be given by Eq.(2) with the boundary conditions Eq.(~). This gives Eq.(5). This indicates that drops can be divided up according to their initial radius - drops between R1 and R1 ~-dR1 will remain similar all their lives and will disappear at the same time ~' Thus the behaviour of each group can be calculated separately and the final result got by ~umming~ Let the initial distribution be described by the function ~(Rl) . Then the number of drops at the initial moment in such a group is: ~(R1)dR1 (6) Extend the function to fl(u, Rl) so that the number of drops in the range (R1, R1 + dRl) at any moment v is equal to: fl(w, R1)dR1 � (7) Card 3/9 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 ~9-58-5-7/15 The Crystallization of Super-cooled Water Clouds by Freezing of Drops. From Eq.(1) we have the number of drops in unit time, from this group, which turn into crystals (Eq.8). Using Eqo(6), it is found that fl(~R1) can be expressed by an integral equation, which is most conveniently expressed in the form Eqo(9)o At a certain moment ~' the considered group dis- appear as a result of evaporation. At this moment R1 is given by Eq.(lO) from Eq.(5). Eq.(lO) permits the initial radius to be expressed in terms of the moment of disappear- ance of the drop (R1 = Z(~') ) . To distinguish one group of similar drops from another group, the initial radius of the drop is used. Crystals must be defined by two para- meters: R1 defining the drops from which they arise and � " the moment of freezing of the drop. The description of the crystallization process in terms of these two variables � s' ~nalogous to the.problems,of hydrodynamics in Lagrangian variables. A function f2(~ , Rl) is introduced so that the number of crystals formed at time ~" from drops with Card 4/9 APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C~A-RDP86-005~3R0002046~00~9-8 Card 5/~ integrating again for '9-58-5-7/15 T~e Crystallization of Super-cooled Water Clouds by Freezing of Drops~ - initial radii in the range R1 to R1 +dR1 is equal to f2(~", R1)dR1 . The number of crystals formed per unit time from this group is given by Eq.(ll). Considering next the equation for the change in concentration of vapour u(~) during crystallization, this change/unit time will be equal to the difference between the total vapour flow from the evaporating drops and total vapour flow to the growing crys- tals, Eq.(12). (P1 is the vapour flow from the drops; P2 is the vapour flow to the crystals)� P1 is first found (Eqol3) and then P2 � This latter can be obtained by in- tegrating Eq.(3) with the boundary conditions (Eq.14), giving Eqo(15) which represents the radius of the crystal as a func- tion of r2(T, T", R1). Eq.(16) gives the flow to a crystal arising at the moment v" . At ~" freeze for which Ri~Z(~') E~ . Therefore Eq.(16) = ~ only those drops can is integrated for R1 between the limits Z(~") and Rlmax v" between the limits 0 and ~ APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C~A-RDP86-005~3R0002046~00~9-8 49-58-5-7/15 The Crystallization of Super-cooled Water Clouds by Freezing of Drops~ Eq~(17) for P2 is obtained. Eq.(12) can be written in the form Eq.(18), using Eqs.(13) and (17). Thus five equations (Eqs~ 57 15~ 9, ll ~d 18) have been obtained for five un- knowns rI , r2 ? nI , n2 and u , which c~ therefore be found and hence the crystallization process studied� The initial boundary conditions for the system are that: u = u~ , f2 = 0 when � = 0 ; ~" = 0 . Eliminating rl~ r2' fl and f2 from Eq.(18) by use of the other equations~ an equation for u is obtained which can be written in the form Eqo(19) (where ~ is a function of u~) depending on the value of u in the range ~0, ~, Eq.(19) can be solved by a numerical method which is discussed below. Taking a small value of � = vI u is calculated linearly in the region ~, Vl~ and du/d~ for the point ~l is calculated from Eqo(19). The process is then repeated until the final value of u is found� Once u has been found, the other u~o~s can be easily Card 6/9 APPROVED FOR RELEASE: 06/08/2000 CTA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 C]:A-RDP86-00513R000204610019-8 ~9-58-5-7/15 The Crystallization of Super-cooled Water Clouds by Freezing of Drops. determined. Assuming these solutions are Eqs.(20),(21), (�2) and (23), then, firstly, it is possible to determine the overall number of drops nl(~) and crystals n2(~) in the cloud at any time and, secondly, to determine the density of distribution by dimensions ~l(~, rl) and ~2(~, r2) at any time - these functions can be found from experiments compara- tively easily. The functions nl(~) and n2(~) are obtained from the definition of the functions fl and f2 ' ~(~, rl) and ~2(~, r2) are obtained by considering ~ group of drops the initial dimensions of which lie in the r~nge Crl, rI + drl~ where drI is given by Eqo(24). The number of drops in this group at the moment � is g(~ R1)dR1 ~ which, using Eq.(24) becomes: dr1 ~(~, ~l) ~p(~, ~l) ~R1 Card 7/9 Eq.(25) gives the number of drops at time = with dimensions APPROVED FOR RELEASE: 06/08/2000 ClA-RDP86-00513R000204610019-8" "APPROVED FOR RELEASE: 06/08/2000 CIA-RDP86-00513R000204610019-8 #9-58-5-7/15 The Crystallization of Super-cooled Water Clouds by Freezing of Drops. in the range Itl, rI +~drl~i o From Eqo(22) it is possible to find R1 = Sl(rl, v.) as follows from Eq~(5). Substitut- ing in Eq.(25) gives '~1~, Si(r1, ~)~ = ~(rl~ t) . At ~im8 t"